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Establishing a Correlation Between Residual Stress and Natural Frequency of Vibration for Electron Beam Butt Weld of AISI 304 Stainless Steel

  • Research Article-Mechanical Engineering
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Abstract

Residual stresses developed during complex multi-physics electron beam welding process are usually detrimental to the joint integrity. Moreover, the natural frequencies of vibration are reported to decrease with an increase in stress value. Not much literature is available on the study of the changes in natural frequency of vibration due to welding stresses. Moreover, such analysis is limited to mathematical modeling and conventional welding processes. Thus, in the present study, residual stresses of the welds corresponding to different heat inputs are measured experimentally using X-ray diffraction machine. A Polytec laser vibrometer–data acquisition system–LabView assembly is used to experimentally determine the natural frequencies of vibration. The novelty of this study lies with the establishment of a correlation between the measured welding stress and natural frequency of vibration. Additionally, the experimentally obtained residual stresses have also been validated through FEM results with satisfactory agreement. Furthermore, a noble approach of stress estimation using the natural frequencies is proposed and tested successfully.

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Abbreviations

C p :

Specific heat

\( h \) :

Maximum heat source spread along the plate thickness

\( I \) :

Beam current

\( k \) :

Thermal conductivity

\( M1 \) :

Mode one natural frequency of vibration

\( M2 \) :

Mode two natural frequency of vibration

\( M3 \) :

Mode three natural frequency of vibration

\( M4 \) :

Mode four natural frequency of vibration

q v :

Volume heat flux

Q :

Total input power

Q s :

Net power acting on the surface

Q v :

Net power acting on the volume

T :

Temperature

t :

Time

U :

Welding speed

\( V \) :

Accelerating voltage

r b :

Beam radius at the workpiece surface

\( r \) :

Instantaneous beam radius

RSIPP :

Residual stress obtained from input process parameters

RSNFV :

Residual stress obtained from natural frequency of vibrations

\( x,y,z \) :

Space coordinates

\( \gamma_{\text{s}} \) :

A surface coefficient

\( \gamma_{\text{v}} \) :

A volume coefficient

η :

Efficiency

ρ :

Density

\( \psi \) :

Angles for stress measurements

DAQ:

Data acquisition

EBW:

Electron beam welding

FFT:

Fast Fourier transformation algorithm

FEM:

Finite element model

GTAW:

Gas tungsten arc welding

NDT:

Nondestructive testing

SS:

Stainless steel

XRD:

X-ray diffraction

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Acknowledgements

The authors are thankful to Prof. A. K. Samantaray, Systems, Dynamics and Control Laboratory, Department of Mechanical Engineering, IIT Kharagpur, India, for allowing us to use the digital laser vibrometer, LabView software and other setups required to carry out the necessary experiments on the measurement of natural frequency of vibration of welded samples. The authors are also grateful to the research scholars, namely Mr. Sebin Jose and Mr. Pankaj Kumar from the Systems, Dynamics and Control Laboratory, Department of Mechanical Engineering, IIT Kharagpur, India, for their immense assistance and support. The authors are also thankful to Mr. Surajit Mondal and the other members from DRDL, Hyderabad, India, for valuable insight into stress measurement. In addition, the authors are thankful to Prof. S. Paul, Department of Mechanical Engineering, IIT Kharagpur, India, for allowing me to conduct stress measurement.

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Authors and Affiliations

  1. Indian Institute of Technology Kharagpur, Kharagpur, India

    Debasish Das

  2. Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Dilip Kumar Pratihar

  3. Department of Metallurgical and Materials Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Gour Gopal Roy

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  1. Debasish Das
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Correspondence to Dilip Kumar Pratihar.

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Das, D., Pratihar, D.K. & Roy, G.G. Establishing a Correlation Between Residual Stress and Natural Frequency of Vibration for Electron Beam Butt Weld of AISI 304 Stainless Steel. Arab J Sci Eng 45, 5769–5781 (2020). https://doi.org/10.1007/s13369-020-04560-0

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